The objective of this paper is to study the representation of neutrosophic matrices defined over a neutrosophic field by neutrosophic linear transformations between neutrosophic vector spaces, where it proves that every neutrosophic matrix can be represented uniquely by a neutrosophic linear transformation. Also, this work proves that every neutrosophic linear transformation must be an AH-linear transformation; i.e., it can be represented by classical linear transformations.

The objective of this paper is to introduce the concept of refined neutrosophic matrices as matrices such as multiplication, addition, and ring property. Also, it determines the necessary and sufficient condition for the invertibility of these matrices with respect to multiplication. On the contrary, nilpotency and idempotency properties will be discussed.

This paper studies classical homomorphisms between n-refined neutrosophic ring and m-refined neutrosophic ring. It proves that every m-refined neutrosophic ring is a homomorphic image of n-refined neutrosophic ring , where . Also, it presents a discussion of kernels and some corresponding isomorphisms between those rings.

American scientific publishing group

The aim of this paper is to study homomorphisms between refined neutrosophic rings and neutrosophic rings. We prove that every neutrosophic ring R(I) is a homomorphic image of the refined neutrosophic ring R(I_1,I_2). Furthermore, we prove the following interesting result:

The objective of this article is to define and study the concepts of refined neurosophic AH-ideal and AHS-ideal in refined neutrosophic rings.We investigate the elementary properties of these concepts.